Fresh off their defeat on the Senate floor Thursday, congressional Republicans pledged to move forward with their efforts to broaden the exemptions from the Obama administration’s contraception coverage rule.

But they were left without a clear strategy for moving ahead, and the fight seemed to have energized Democrats, who welcomed the debate as a chance to win over independent women during an election year.

The most likely path ahead is in the House. At a press conference shortly before the Senate vote, House Speaker John Boehner said he’s still looking at options for overturning the Obama administration’s policy.

He didn’t mention a bill introduced months ago by Rep. Jeff Fortenberry (R-Neb.) that would overturn the coverage requirements. A Fortenberry spokeswoman told POLITICO that Boehner had promised to move the bill during a Tuesday meeting of the Republican Conference.

The Senate narrowly defeated a measure by Missouri Republican Roy Blunt that would have allowed employers to refuse to cover health services if they had moral objections. The vote to table the measure — an amendment to the transportation bill — was 51-48, with retiring Sen. Olympia Snowe (R-Maine) joining most Democrats to oppose the amendment.

But all of the other Republicans stuck together to support it — including Sen. Scott Brown of Massachusetts, who’s getting pounded by Democrats over his support for the measure as he runs for reelection. Three Democrats — Sens. Ben Nelson of Nebraska, Joe Manchin of West Virginia and Bob Casey of Pennsylvania — joined Republicans in support of the amendment.

Republicans still hope to frame the debate as an issue of religious freedom, not contraception — an argument for which they believe they have a stronger hand.

Blunt vowed that Thursday’s vote won’t be the end of the debate over the contraception coverage rule — and predicted that the Supreme Court might have the final say by striking it down.

“This issue will not go away unless the administration takes it away by giving people of faith those First Amendment protections” to refuse to cover services if they have moral or religious objections, Blunt said during the floor debate.

While Senate Democrats praised their effort to block the measure on Thursday, they pledged to continue talking about it.

“We will make sure that women across the country are aware of what the Republicans in the Senate propose to do,” Sen. Chuck Schumer (D-N.Y.) told reporters on Capitol Hill. “If Republicans keep this up, they’re going to drive away independent voters — women and men — just as they’re driving moderates out of their caucus.”

“I think it’s going to be awfully hard to defend it back home, especially in places like New England,” Schumer said in a veiled shot at Brown.

In fact, Brown’s opponent, Elizabeth Warren, blasted out a statement Thursday saying the Senate “did the right thing in stopping Scott Brown and his extreme amendment that threatened health care coverage for women and families.”

“It’s time to end the culture wars and get to work for the middle class. Time to elect more women to the U.S. Senate,” the video said. “If you don’t like what Republicans are doing, send a woman to the Senate. In fact, send them all.”

President Barack Obama’s campaign weighed in, too, posting on its Tumblr account a mock permission slip from an employer granting a female employee access to contraceptives.

Republicans defended the proposal, arguing that it isn’t about contraceptives. Rather, they want to ensure that no employer has to pay for an insurance policy that provides coverage of anything to which they morally object.

“Nobody is taking anything away from anybody,” Sen. Orrin Hatch (R-Utah) said. “It’s a moral and religious issue that should not be interfered with by the federal government.”

And Mitt Romney — who fumbled a question from an Ohio reporter Wednesday by seeming to say he opposed the Blunt amendment, only to later say that he misunderstood the question — was firmly in the religious freedom camp Thursday.

“I applaud the Senators who took a stand today and voted to defend religious freedom,” Romney said in a statement after the vote. “The Obama Administration has directly attacked the First Amendment of our Constitution and individual liberty. The President of the United States must protect and defend the Constitution, not ignore it.”

The Senate vote was largely along partisan lines.

Moderate Sens. Susan Collins (R-Maine) and Lisa Murkowski (R-Alaska) voted with the rest of the Republicans to move forward with the bill. Both Collins and Murkowski voiced some reservations about the vote.

Collins said she asked the Department of Health and Human Services to clarify how self-insured religious-affiliated institutions would fare under the policy. She said she got no clear answer. “I feel I have no choice,” she said of her vote for the Blunt amendment.

The administration had a few Democratic critics, too. Manchin, who is facing voters this fall, and Nelson, who is retiring, said the Obama administration’s policy doesn’t ensure that religious freedoms are protected.

Blunt said the vote that defeated his amendment went “just as he expected it to go.”

“I’m pleased it was bipartisan, I’m pleased that three Democrats were supportive. It’s a matter of conscience; people have to do what they have to do on something like this,” he said. “I’m confident this issue is not over and won’t be over until the administration figures out how to accommodate people’s religious views as it relates to these new mandates.”

The United States Conference of Catholic Bishops praised the close vote and pledged to take the fight to the House as it seeks to have the rule struck down through “all available legal means.”

In a statement, USCCB Religious Liberty Committee Chairman Bishop William Lori said, “We will build on this base of support as we pursue legislation in the House of Representatives, urge the Administration to change its course on this issue, and explore our legal rights under the Constitution and the Religious Freedom Restoration Act.”

In the House, no committee has yet taken up a bill on the issue. Boehner said Thursday that he’s looking for a solution that could get bipartisan support.

“I think it’s important for us to win this issue,” he stressed. “The government, our government, for 220 years has respected the religious views of the American people, and for all of this time there’s been an exception for those churches and other groups to protect the religious beliefs. … That’s being violated here.”

In a poll released Thursday, the Kaiser Family Foundation found that 63 percent of respondents support the Obama administration’s requirement for private health insurance plans to cover the cost of contraception, while only 33 percent oppose it. Other polls have found the public to be more closely divided over the rule.